Abstract: We consider parabolic semigroups of holomorphic self-maps of the unit disk with Denjoy-Wolff point , Koenigs function and associated planar domain . We give a geometric description of the classification of such semigroups: The semigroup is of positive hyperbolic step if and only if is contained in a horizontal half-plane. Moreover, a semigroup of positive hyperbolic step has trajectories that converge to strongly tangentially (namely the semigroup is of finite shift) if and only if is conformal at .